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This paper introduces a rigorous framework for function modeling of complex multidisciplinary systems based on the system state flow diagram (SSFD). The work addresses the need for a consistent methodology to support solution-neutral function-based system decomposition analysis, facilitating the design, modeling, and analysis of complex systems architectures. A rigorous basis for the SSFD is established by defining conventions for states and function definitions and a representation scheme, underpinned by a critical review of existing literature. A set of heuristics are introduced to support the function decomposition analysis and to facilitate the deployment of the methodology with strong practitioner guidelines. The SSFD heuristics extend the existing framework of Otto and Wood (2001) by introducing a conditional fork node heuristic, to facilitate analysis and aggregation of function models across multiple modes of operation of the system. The empirical validation of the SSFD function modeling framework is discussed in relation to its application to two case studies: a benchmark problem (glue gun) set for the engineering design community; and an industrial case study of an electric vehicle powertrain. Based on the evidence from the two case studies presented in the paper, a critical evaluation of the SSFD function modeling methodology is discussed based on the function benchmarking framework established by Summers et al. (2013), considering the representation, modeling, cognitive, and reasoning characteristics. The significance of this paper is that it establishes a rigorous reference framework for the SSFD function representation and a consistent methodology to guide the practitioner with its deployment, facilitating its impact to industrial practice.

Dealing with component interactions and dependencies remains a core and fundamental aspect of engineering, where conflicts and constraints are solved on an almost daily basis. Failure to consider these interactions and dependencies can lead to costly overruns, failure to meet requirements, and lengthy redesigns. Thus, the management and monitoring of these dependencies remains a crucial activity in engineering projects and is becoming ever more challenging with the increase in the number of components, component interactions, and component dependencies, in both a structural and a functional sense. For these reasons, tools and methods to support the identification and monitoring of component interactions and dependencies continues to be an active area of research. In particular, design structure matrices (DSMs) have been extensively applied to identify and visualize product and organizational architectures across a number of engineering disciplines. However, the process of generating these DSMs has primarily used surveys, structured interviews, and/or meetings with engineers. As a consequence, there is a high cost associated with engineers' time alongside the requirement to continually update the DSM structure as a product develops. It follows that the proposition of this paper is to investigate whether an automated and continuously evolving DSM can be generated by monitoring the changes in the digital models that represent the product. This includes models that are generated from computer-aided design, finite element analysis, and computational fluid dynamics systems. The paper shows that a DSM generated from the changes in the product models corroborates with the product architecture as defined by the engineers and results from previous DSM studies. In addition, further levels of product architecture dependency were also identified. A particular affordance of automatically generating DSMs is the ability to continually generate DSMs throughout the project. This paper demonstrates the opportunity for project managers to monitor emerging product dependencies alongside changes in modes of working between the engineers. The application of this technique could be used to support existing product life cycle change management solutions, cross-company product development, and small to medium enterprises who do not have a product life cycle management solution.

Communication is both the problem and the solution to misunderstanding. It is the human communicative ability to display understanding to resolve misunderstandings that plays an important part in the organization of the design inputs to a construction project. Ambiguity and uncertainty, as different forms of misunderstanding, are studied in this article, as they are manifest in the conversation at a design meeting. In this setting the coordination of both in situ design activities and the planning of design tasks takes place in real time, in conversation. Exhibited are several ways that design ambiguities and uncertainties can be seen in the interactional details of a multidisciplinary design team's conversation, to then report on how different design expertise featured in the raising of, and attempts at resolving, the misunderstandings that arose. In the course of this meeting, ambiguity and uncertainty were observed not as neat, discrete phenomena but were interwoven in the conversation. This characteristic poses difficulties in the disambiguation of the problem-solving response to each form of misunderstanding and further develops our understanding of design as it is communicated and conducted in social interaction. Finally, some implications from this study are put forward to inform the design of support for collaborative design.

This paper defines a number of general operations that accept arbitrary sets of values for two variables and general relations among three variables and generate a variety of third sets that are useful in design. Although the operations are defined without respect to mathematical or engineering domain, computing these operations depends on the specific mathematical domain, and algorithms are available for only a few domains. Appropriate software could make this complexity transparent to the designer, allowing the same conceptual operations to be used in many contexts. The paper proves a number of useful characteristics of the operations and offers examples of their potential use in design.

Shape annealing, a computational design method applied to structural design, has been extended to the design of traditional and innovative three-dimensional domes that incorporate the design goals of efficiency, economy, utility, and elegance. In contrast to deterministic structural optimization methods, shape annealing, a stochastic method, uses lateral exploration to generate multiple designs of similar quality that form a structural language of solutions. Structural languages can serve to enhance designer creativity by presenting multiple, spatially innovative, yet functional design solutions while also providing insight into the interaction between structural form and the trade-offs involved in multi-objective design. The style of the structures within a language is a product of the shape grammar that defines the allowable structural forms and the optimization model that provides a functional measure of the generated forms to determine the desirable designs. This paper presents an application of geodesic dome patterns that have been embodied in a shape grammar to define a structural language of domes. Within this language of domes, different dome styles are generated by changing the optimization model for dome design to include the design goals of maximum enclosure space, minimum surface area, minimum number of distinct cross-sectional areas, and visual uniformity. The strengths of the method that will be shown are 1) the generation of both conventional domes similar to shape optimization results and spatially innovative domes, 2) the generation of design alternatives within a defined design style, and 3) the generation of different design styles by modifying the language semantics provided by the optimization model.

This paper defines, for use in design, rules for propagating “distribution constraints” through relationships such as algebraic or vector equations. Distribution constraints are predicate logic statements about the values that physical system parameters may assume. The propagation rules take into account “variation source causality”: information about when and how the values are assigned during the design, manufacturing, and operation of the system.

Physical systems can be modelled at many levels of approximation. The right model depends on the problem to be solved. In many cases, a combination of models will be more effective than a single model. Our research investigates this idea in the context of engineering design optimization. We present a family of strategies that use multiple models for unconstrained optimization of engineering designs. The strategies are useful when multiple approximations of an objective function can be implemented by compositional modelling techniques. We show how a compositional modelling library can be used to construct a variety of locally calibratable approximation schemes that can be incorporated into the optimization strategies. We analyze the optimization strategies and approximation schemes to formulate and prove sufficient conditions for correctness and convergence. We also report experimental tests of our methods in the domain of sailing yacht design. Our results demonstrate dramatic reductions in the CPU time required for optimization, on the problems we tested, with no significant loss in design quality.

This paper is concerned with presenting guidelines to aide in the selection of the appropriate network architecture for back-propagation neural networks used as approximators. In particular, its goal is to indicate under what circumstances neural networks should have two hidden layers and under what circumstances they should have one hidden layer. Networks with one and with two hidden layers were used to approximate numerous test functions. Guidelines were developed from the results of these investigations.

The combination of the paradigms of shape algebras and predicate logic representations, used in a new method for describing designs, is presented. First-order predicate logic provides a natural, intuitive way of representing shapes and spatial relations in the development of complete computer systems for reasoning about designs. Shape algebraic formalisms have advantages over more traditional representations of geometric objects. Here we illustrate the definition of a large set of high-level design relations from a small set of simple structures and spatial relations, with examples from the domains of geographic information systems and architecture.

The “sketch” drawn by a human designer represents a shape class of wider variability than can be captured by traditional CAD models; these typically work with parametrizations based on a nearly finished shape. Traditional Qualitative Reasoning is also unable to model this degree of ambiguity in shape. Cognitively, shapes are often represented in terms of an axial model. In defining 2D contours, such an axial representation is called the Medial Axis Transform or MAT. By perturbing the parameters of the MAT—length, link angle, and the node radius—one can define a shape class. Unlike the contour-to-MAT transform, which is well-known to be unstable, the MAT-to-contour process is an integrative process and is very stable. The variation in these parameters can be controlled by defining a suitable discretization over the parameter space. This leads to a broad class of similar shapes from which an optimized shape can be obtained for a given set of criteria. The optimizing criteria may involve the boundary description for each shape; the axial model is only used for generating the shape class. This Qualitative MAT model has been tested in several design optimization contexts, using Genetic Algorithms, and we show results for Automobile contours, IC engine parts, building profiles, etc.

Few existing Computer Aided Design (CAD) systems provide assistance to designers in developing geometric concepts at the early design stages. Instead they require a high level of precision and detail suited to detail design. To support the early geometric design, a CAD system should provide utilities for the rapid capture and iterative development of vague geometric models. This paper presents a pilot system that is being developed based on such a vision. The system has adopted minimum commitment modelling and incremental refinement as the guiding principles. The representation of geometric configuration is based on a parametric and constraint-based geometric design model, and provides a uniform representation of the approximate and precise size and location parameters. A constraint-based mechanism has been developed for processing geometric information. The use of the system in assisting the development of a geometric configuration is also demonstrated. Finally, features and limitations of the system as well as relations to relevant works are discussed, and based on this a number of key research directions are established.

The geometric dimensioning and tolerancing (GD&T) specifications of a design are directly associated with its performance and functional requirements. They also govern the manufacturing and quality control processes needed to achieve those requirements. This paper reviews recent work in geometric tolerance representation and reasoning and presents a generic and uniform graph-based representation scheme, called the Tolerance Network, to represent GD&T specifications across a part or assembly. The network can accommodate GD&T specifications related to the function, behavior, manufacturing, and inspection requirements embedded in design specifications and supports the use of different types of tolerances. The network also accommodates common design practices such as the specification of overconstrained features and parts. The necessary properties of such a network are discussed that allow under- and overconstrained design specifications to be detected and analyzed.

The spatial synthesis problem addressed in this paper is the configuration of rectangles in 2D space, where the sides of the rectangles are parallel to an orthogonal coordinate system. Variables are the locations of the edges of the rectangles and their orientations. Algebraic constraints on these variables define a layout and constitute a constraint satisfaction problem. We give a new O(n2) algorithm for incremental path-consistency, which is applied after adding each algebraic constraint. Problem requirements are formulated as spatial relations between the rectangles, for example, adjacency, minimum distance, and nonoverlap. Spatial relations are expressed by Boolean combinations of the algebraic constraints; called disjunctive constraints. Solutions are generated by backtracking search, which selects a disjunctive constraint and instantiates its disjuncts. The selected disjuncts describe an equivalence class of configurations that is a significantly different solution. This method generates the set of significantly different solutions that satisfy all the requirements. The order of instantiating disjunctive constraints is critical for search efficiency. It is determined dynamically at each search state, using functions of heuristic measures called textures. Textures implement fail-first and prune-early strategies. Extensions to the model, that is, 3D configurations, configurations of nonrectangular shapes, constraint relaxation, optimization, and adding new rectangles during search are discussed.

This paper proposes a new method for dealing with geometrical layout constraints. Geometrical layout constraints are classified into three classes of dimensional, regional, and interference constraints. Dimensional constraints are handled by using an existing methodology. A method is proposed to translate the other two classes of constraints into dimensional constraints. Thus, it is possible to uniformly deal with all of those geometrical layout constraints. The method is twofold. First, it converts regional, interference constraints into a set of simple inequalities. Then each inequality is solved by a geometric gadget, which is a structured set of dimensional constraints. A prototype system is developed and applied to some layout design examples.

Because mechanical operations are performed only up to a certain precision, the geometry of parts involved in real-life products is never known precisely. But if tolerance models for specifying acceptable variations have received a substantial attention, operations on toleranced objects have not been studied extensively. That is the reason why we address in this paper the computation of the union and the intersection of toleranced simple polygons, under a simple and already known tolerance model. First, we provide a practical and efficient algorithm that stores in an implicit data structure the information necessary to answer a request for specific values of the tolerances without performing a computation from scratch. If the polygons are of sizes m and n, and s is the number of intersections between edges occurring for all the combinations of tolerance values, the preprocessed data structure takes O(s) space and the algorithm that computes a union/intersection from it takes O((n + m)log s + k' + k log k) time, where k is the number of vertices of the union/intersection and k ≤ k' ≤ s. Although the algorithm is not output sensitive, we show that the expectations of k and k' remain within a constant factor τ, a function of the input geometry. Second, we define and study the stability of union or intersection features. Third, we list interesting applications of the algorithms related to feasibility of assembly and assembly sequencing of real assemblies.